Abstract
The use of computational complexity in planning, and in AI in general, has always been a disputed topic. A major problem with ordinary worst-case analyses is that they do not provide any quantitative information: they do not tell us much about the running time of concrete algorithms, nor do they tell us much about the running time of optimal algorithms. We address problems like this by presenting results based on the exponential time hypothesis (ETH), which is a widely accepted hypothesis concerning the time complexity of 3-SAT. By using this approach, we provide, for instance, almost matching upper and lower bounds onthe time complexity of propositional planning.
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References
Bäckström, C., Jonsson, P.: All PSPACE-complete planning problems are equal but some are more equal than others. In: Proceedings 4th Annual Symposium on Combinatorial Search (SOCS-11), pp 10–17, Barcelona, Spain (2011)
Bäckström, C., Jonsson, P.: Algorithms and limits for compact plan representations. J. Artif. Intell. Res. 44, 141–177 (2012)
Bäckström, C., Jonsson, P.: A refined view of causal graphs and component sizes: SP-closed graph classes and beyond. J. Artif. Intell. Res. 47, 575–611 (2013)
Bäckström, C., Jonsson, P., Ordyniak, S., Szeider, S.: A complete parameterized complexity analysis of bounded planning. J. Comput. Syst. Sci., 1311–1332 (2015)
Bäckström, C., Jonsson, P., Ståhlberg, S.: Fast detection of unsolvable planning instances using local consistency. In: Proceedings 6th Annual Symposium on Combinatorial Search (SOCS-13), pp 29–37, WA, USA (2013)
Bäckström, C., Nebel, B.: Complexity results for SAS + planning. Comput. Intell. 11, 625–656 (1995)
Bogomolov, S., Magazzeni, D., Podelski, A., Wehrle, M.: Planning as model checking in hybrid domains. In: Proceedings 28th AAAI Conference on Artificial Intelligence (AAAI-14), pp 2228–2234, QC, Canada (2014)
Bylander, T.: The computational complexity of propositional STRIPS planning. Artif. Intell. 69(1-2), 165–204 (1994)
Chen, J., Chor, B., Fellows, M., Huang, X., Juedes, D.W., Kanj, I.A., Xia, G.: Tight lower bounds for certain parameterized NP-hard problems. Inf. Comput. 201(2), 216–231 (2005)
Chen, J., Huang, X., Kanj, I., Xia, G.: Strong computational lower bounds via parameterized complexity. J. Comput. Syst. Sci. 72(8), 1346–1367 (2006)
Chen, Y., Grohe, M.: An isomorphism between subexponential and parameterized complexity theory. SIAM J. Comput. 37(4), 1228–1258 (2007)
Garey, M.R., Johnson, D.S.: Computers and intractability: a guide to the theory of NP-completeness (1979)
Helmert, M.: Complexity results for standard benchmark domains in planning. Artif. Intell. 143(2), 219–262 (2003)
Hoffmann, J., Kissmann, P., Torralba, Á.: Distance? Who cares? Tailoring merge-and-shrink heuristics to detect unsolvability. In: Proceedings 21st European Conference on Artificial Intelligence (ECAI-2014), pp 441–446 (2014)
Impagliazzo, R., Paturi, R.: On the complexity of k-SAT. J. Comput. Syst. Sci. 62(2), 367–375 (2001)
Impagliazzo, R., Paturi, R., Zane, F.: Which problems have strongly exponential complexity. J. Comput. Syst. Sci. 63(4), 512–530 (2001)
Jonsson, P., Bäckström, C.: Tractable plan existence does not imply tractable plan generation. Ann. Math. Artif. Intell. 22(3-4), 281–296 (1998)
Jonsson, P., Lagerkvist, V., Nordh, G., Zanuttini, B.: Complexity of SAT problems, clone theory and the exponential time hypothesis. In: Proceedings 24th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA-13), pp 1264–1277, LA, USA (2013)
Kanj, I., Szeider, S.: On the subexponential time complexity of CSP. In: Proceedings 27th AAAI Conference on Artificial Intelligence (AAAI-13), pp 459–465, WA, USA (2013)
Levesque, H.: Logic and the complexity of reasoning. J. Philos. Log. 17(4), 355–389 (1988)
Linares López, C., Celorrio, S.J., Olaya, A.G.: The deterministic part of the seventh international planning competition. Artif. Intell. 223, 82–119 (2015)
Lokshtanov, D., Marx, D., Saurabh, S.: Lower bounds based on the exponential time hypothesis. B. EATCS 105, 41–72 (2011)
Marx, D.: On the optiMality of planar and geometric approximation schemes. In: Proceedings 48th Annual IEEE Symposium on Foundations of Computer Science (FOCS-07), pp 338–348, RI, USA (2007)
Rintanen, J.: Generation of hard solvable planning problems. Technical report TR-CS-12-03, College of Engineering and Computer Science, The Australian National University, Canberra, Australia (2012)
Santhanam, R., Srinivasan, S.: On the limits of sparsification. In: Proceeding of the 39th International Colloquium on Automata, Languages, and Programming (ICALP-12), pp 774–785, Warwick, UK (2012)
Savitch, W.: Relationships between nondeterministic and deterministic tape complexities. J. Comput. Syst. Sci. 4(2), 177–192 (1970)
Sipser, M.: Introduction to the theory of computation, 2nd edn. Thomson Course Technology (2006)
Stearns, R.E.: Turing award lecture: It’s time to reconsider time. Commun. ACM 37(11), 95–99 (1994)
Stearns, R.E.: Deterministic versus nondeterministic time and lower bound problems. J. ACM 50(1), 91–95 (2003)
Stearns, R.E., Hunt, III, H.B.: Power indices and easier hard problems. Math. Syst. Theory 23(4), 209–225 (1990)
Traxler, P.: The time complexity of constraint satisfaction. In: Proceeding of the 3rd International Workshop on Parameterized and Exact Computation (IWPEC-08), pp 190–201, BC, Canada (2008)
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Meysam Aghighi and Simon Ståhlberg are partially supported by the National Graduate School in Computer Science (CUGS), Sweden. Christer Bäckström is partially supported by the Swedish Research Council (VR) under grant 621-2014-4086.
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Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
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Aghighi, M., Bäckström, C., Jonsson, P. et al. Refining complexity analyses in planning by exploiting the exponential time hypothesis. Ann Math Artif Intell 78, 157–175 (2016). https://doi.org/10.1007/s10472-016-9521-y
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DOI: https://doi.org/10.1007/s10472-016-9521-y